Abstract

"A general analysis of all possible cavity shapes is given with a discussion of the mathematical difficulties involved for the various cases. Special emphasis is given to cavity shapes describable in terms of the coordinate surfaces of coordinate systems separating the scalar wave equation. 112 such shapes are identified and discussed. Free boundary condition equations for spheres and spheroids are derived in complete generality in terms of potentials. The difference in the vibrations of a solid and those of a cavity of the same shape is discussed and made clear. The impossibility of deriving a frequency equation for uniform radial vibrations of spherical cavities as a function of cavity size, alone, is proven. Frequency equations are derived for the standing waves between a plane free surface and radially vibrating cavities of spherical and spheroidal shapes. The frequency spectrum, for this mode of vibration, is shown to be a function of cavity size, shape, depth, and orientation. Suggestions are given for further research in cavity resonance" – Abstract, page ii.